I was wondering if there is a way to tell the compression ratio on a assembled engine

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SOOOOO much money spent and I keep gettin' told that I could have had a V-8

Only if you measured all the relevant parameters before assembling it: Bore, stroke, piston deck height, combustion chamber volume, cylinder head gasket bore and compressed thickness.

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一期一会
Too many people who were born on third base actually believe they've hit a triple.

You need to dis-assemble and measure everything in order to get an accurate static compression ratio number.
For an assembled engine, test the dynamic compression ratio (cranking pressure in psi) and "leak-down" rate... that can tell you a lot about your combination.
DD